Finite Group Databasebeta

← #16780724

Subgroups — #16780724

Order 3328.

528 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130621C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3C2×#11718303C212yesmaximal
4#13129714C212yesmaximal
5C4×#88198C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×#88198C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×#88112C2212yes—
10C2×#88112C2212yes—
11C2×#88110—21no—
12C2×C4×#1057—21no—
13#11718891C411yescharacteristic
14#11718637C2211yescharacteristic
15#11718635C411yescharacteristic
16#11718633—21no—
17#11718633—21no—
18C4×#6101—21no—
19C4×#6101—21no—
20C42×Dic13C2211yescharacteristic
21#11718303C418yescomplemented
22#11718290—21no—
23#11718290—21no—
24C22×Q8×C13C2×C411yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C4×Q8×C13—42no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13C2×C411yescharacteristic
33#88198—22no—
34#88198C2×C414yes—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13C2311yescharacteristic
48C4×Dic26—42no—
49#88112—22no—
50#88112—22no—
51#88112C2×C414yes—
52#88112C2×C414yes—
53#88110—42no—
54C4×#1057—42no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#8235—131nomaximal, Sylow
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13C4212yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26C4212yes—
79C2×#1057—24no—
80C2×#1057—24no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C42×C13—22no—
88C42×C13—42no—
89C4⋊Dic13—41no—
90#6101—24no—
91#6101—24no—
92#6101—42no—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96C4×Dic13—22no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—22no—
100C4×Dic13—41no—
101C4×Dic13—42no—
102C4×Dic13SD1612yes—
103C4×Dic13Q1612yes—
104C4×Dic13C22×C412yes—
105C4×Dic13#4112yes—
106C4×C4⋊Q8—131no—
107#1767—131no—
108C4×C4⋊C8—131no—
109C2×#333—132no—
110#1296—132no—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—42no—
113Q8×C13—42no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13#10012yes—
127C2×C4×C13#10312yes—
128C2×C4×C13C2×C4211yescharacteristic
129C2×C4×C13#11711yescharacteristic
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—22no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13#10312yes—
142C2×Dic13C4×D412yes—
143C2×Dic13C4×D412yes—
144C2×Dic13C2×SD1611yescharacteristic
145C2×Dic13C2×Q1611yescharacteristic
146C2×Dic13#13512yes—
147C2×Dic13AGL(1,ℤ/8)11yescharacteristic
148C2×Dic13#13712yes—
149C2×Dic13#13711yescharacteristic
150Dic26—42no—
151Dic26—42no—
152#1057—44no—
153#1057—44no—
154C2×C4⋊Q8—131no—
155C2×C4×Q8—131no—
156C2×C4×Q8#26111yescharacteristic
157C2×C4⋊C8—132no—
158C2×C4⋊C8—132no—
159C2×#97—261no—
160C2×C4×C8—261no—
161#391—131no—
162#391—131no—
163#389—261no—
164#389—261no—
165#384—131no—
166C4×C4⋊C4—261no—
167C4×C4⋊C4—261no—
168C43—131no—
169#336—261no—
170#336—261no—
171#333—138no—
172C22×C13C4×C22⋊C411yescharacteristic
173C22×C13C2×#10011yescharacteristic
174C22×C13#41311yescharacteristic
175C22×C13C2×#10311yescharacteristic
176C22×C13#41611yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13#41911yescharacteristic
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—42no—
184C4×C13—81no—
185Dic13—22no—
186Dic13—41no—
187Dic13—42no—
188Dic13—81no—
189Dic13C4×SD1612yes—
190Dic13C4×Q1612yes—
191Dic13#44012yes—
192Dic13#44112yes—
193C22×Q8—131no—
194C22×Q8C2×#26111yescharacteristic
195C22×C8—262no—
196C22×C8—262no—
197C4⋊Q8—134no—
198C4⋊Q8—262no—
199C4×Q8—42no—
200C4×Q8—522no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C2×#26111yescharacteristic
209C2×C42—21no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—261no—
217C2×C42C2×#26111yescharacteristic
218C4⋊C8—134no—
219C4⋊C8—134no—
220C4⋊C8—262no—
221C4⋊C8—262no—
222#97—522no—
223C4×C8—522no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13#154811yescharacteristic
229C2×C13#155011yescharacteristic
230C2×C13#155111yescharacteristic
231C2×C13#155411yescharacteristic
232C2×C13C4×#10011yescharacteristic
233C2×C13C4×#10311yescharacteristic
234C2×C13#176311yescharacteristic
235C2×Q8—21no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—132no—
239C2×Q8—261no—
240C2×Q8—521no—
241C2×Q8—521no—
242C2×Q8C4×#26112yes—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4C22⋊#26111yescharacteristic
252C22×C4C22⋊#26111yescharacteristic
253C22×C4C22×#26111yescharacteristic
254C2×C8—264no—
255C2×C8—264no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—264no—
263C4⋊C4—264no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—522no—
268C4⋊C4—522no—
269C42—22no—
270C42—42no—
271C42—132no—
272C42—132no—
273C42—132no—
274C42—132no—
275C42—261no—
276C42—262no—
277C42—261no—
278C42—262no—
279C42—521no—
280C42—522no—
281C13#823511yescharacteristic, complemented, Sylow
282C23C2×C22⋊#26111yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—522no—
286Q8—522no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—132no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—262no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4#8811712yes—
320C2×C4#8812112yes—
321C2×C4C2×C4×#26111yescharacteristic
322C2×C4#8823711yescharacteristic
323C8—524no—
324C8—524no—
325C22#1171913211yescharacteristic
326C22C4×C22⋊#26111yescharacteristic
327C22C2×#8811711yescharacteristic
328C22#1171915311yescharacteristic
329C22#1171916411yescharacteristic
330C22#1171916511yescharacteristic
331C22C2×#8812111yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—42no—
337C4—81no—
338C4—132no—
339C4—132no—
340C4—132no—
341C4—132no—
342C4—262no—
343C4—522no—
344C4—521no—
345C4—1041no—
346C2#1313034911yescharacteristic
347C2#1313035311yescharacteristic
348C2#1313035511yescharacteristic
349C2#1313036111yescharacteristic
350C2C4×#8812111yescharacteristic
351C2C4×#8811711yescharacteristic
352C2#1313060811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#8235
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
21. #11718303C4semidirect
281. C13#8235semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131306212
C4×#881122
C2×#117183032
#131297142
C4×#881982
#823513